var img = new Image();

var $el = $('body');

var containHeight = null;

var containWidth = null;

var containImg = {

  w: null,

  h: null

};

var bkgImgDims = null;

img.src = $el.css('background-image').replace(/url\(\"|\"\)$/ig, "");

​

var bgImgWidth = img.width;

var bgImgHeight = img.height;

​

var imgProportionalH = Math.abs(bgImgHeight / bgImgWidth);

var imgProportionalW = Math.abs(bgImgWidth / bgImgHeight);

​

​

function getElProportions() {

  var elW = $el.width();

  var elH = $el.height();

  var elProportionalH = Math.abs(elH / elW);

  var elProportionalW = Math.abs(elW / elH);

​

  // If the element is shorter than the width of the image

  if(elProportionalH < imgProportionalH) {

    containImg.h = elH;

    containImg.w = Math.abs( elH / imgProportionalH );

  } else {

    containImg.h = Math.abs( elW / imgProportionalW );

    containImg.w = elW;

  }

  return containImg;

}

​

​

$(document).ready(function(){

  bkgImgDims = getElProportions();

  console.log(bkgImgDims);

});

​

$(window).resize(function(){

  bkgImgDims = getElProportions();

  console.log(bkgImgDims);

});